Metamath Proof Explorer

Theorem pm2.8

Description: Theorem *2.8 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Jan-2013)

Ref Expression
Assertion pm2.8 
|- ( ( ph \/ ps ) -> ( ( -. ps \/ ch ) -> ( ph \/ ch ) ) )

Proof

Step Hyp Ref Expression
1 pm2.53 
 |-  ( ( ph \/ ps ) -> ( -. ph -> ps ) )
2 1 con1d 
 |-  ( ( ph \/ ps ) -> ( -. ps -> ph ) )
3 2 orim1d 
 |-  ( ( ph \/ ps ) -> ( ( -. ps \/ ch ) -> ( ph \/ ch ) ) )